About Twist

     Rifles and pistols, and some shotguns, have "rifled" barrels. Spiral grooves are formed in the bore of the barrel in order to stabilize the bullet. These grooves are called "rifling". Stabilization causes the bullet to move point-forward through the air, without tumbling or wobbling.

     "Twist" is the rate at which the grooves rotate in the bore of the barrel; twist or turn as they extend down the bore.. If these grooves turn one revolution in ten inches, the twist is said to be "one turn in ten inches" or "ten inch twist". We say that a ten inch twist is "faster" than a fourteen inch twist; that an eighteen inch twist is "slower" than a sixteen inch twist.

     "Gain" twist starts slow at the breech end of the barrel and gradually gets faster until the twist at the muzzle is as fast as required for the cartridge/bullet combination. The reasons given for rifling a barrel with a gain twist are that the action of the lands on the bullet cause a tight seal between the barrel and the bullet; and that the imparting of rotation to the bullet is easier or less abrupt and stressful.

Muzzle loading target were sometimes rifled with a gain twist, as were single shot rifles barreled by custom barrel makers, notably Harry M. Pope.

     A gain twist barrel can be made only with cut rifling, button rifling and swaged rifling methods cannot be used. Some single shot shooters claim that cut rifled barrels are most accurate-other, excellent shooters shoot small groups and large scores with button rifled barrels.

     A gain twist barrel cannot be lapped to smooth the interior finish, since the twist varies and no lap fits. Some consider this a problem, Pope said that he did not lap his barrels.

     No consensus has been reached in the last hundred and fifty years about gain twist; excellent shooters take both sides of the argument.

     The twist required to stabilize a bullet is primarily determined by the length and caliber of the bullet. The underlying assumptions about twist are that the bullets are of lead, lead alloy, or another material of similar density; and that the bullets are traveling through air.

     Minor variables affecting the required rate of twist are muzzle velocity (faster bullets allow a slightly slower minimum twist), bullet density (less dense bullets require a slightly faster minimum twist) and air density (less dense air as is found at higher altitudes allows a slightly slower twist).

     The quality of the bullet and barrel are sometimes said to affect the minimum required twist, better quality allowing slower twist.

     George Greenhill was a mathematics lecturer at Emanuel College, Cambridge, England. He developed a formula to estimate the required twist as a function of caliber and bullet length; known as the "Greenhill Formula". (The Greenhill Formula is shown several times below.) It has become common for shooters of a more mathematical bent to criticize, modify and propose alternatives to the Greenhill Formula, and I suppose that for certain applications that is proper. For the vast majority of applications, Greenhill works just fine.

     "Required" twist for a given set of variables is the minimum twist required to stabilize the bullet. For example, the Greenhill formula tells us that for a .308" diameter bullet 1.42" long, the required twist is 10". This means that a 10" twist will stabilize that bullet, or any shorter bullet. It means that any twist less than 10" will not stabilize that bullet, so a 12" twist barrel will not stabilize the bullet.

Over stabilization

     Let's take another Greenhill example: a .224" diameter bullet .84" long will be stabilized by a barrel with a 9" twist. Many 22 caliber bullets are shorter than .84". How does this fast twist affect them? Would a much shorter bullet be "over stabilized"? Some shooters say so. My experience, mostly with 30 caliber rifles, is that nothing VERY bad happens when I shoot short bullets in a 10" twist .308" barrel or a 9" twist .224" barrel. Perhaps the better shooters with better equipment can see the difference; I haven't yet.

     The standard method of calculating the minimum twist required is with the Greenhill formula. There are other calculating methods, some included here.

     There is an EXCEL workbook in the Appendix called "GREENHILL FORMULA WORKBOOK" that has tables and a calculator for GREENHILL variables. With this workbook you can insert any alternative to the Greenhill constant (150) and calculate the twist required for a given caliber/bullet length; or calculate the maximum bullet length for a given caliber/twist.

     There is another EXCEL workbook in the Appendix called "C. DELL'S TWIST FORMULA WORKBOOK" that offers another method.

     And see all below for other opinions and methods.

"Date: 12-8-2005

     I think because lead bullets have such a long bearing surface from nose to base you can use a 1-15 twist barrel to shoot 200 gr bullets up to 1.200 long  at velocity of 1900 fps and above. I only tested these bullets up to 200 Yds.

     About 5 years ago I started testing the 6 PPC case opened up to 30 caliber using bullet weights from 180 to 215 gr in a 1-14 twist barrel. I shot approximately 5,000 bullets in this test. What I found was the accuracy was as good if not a little better than any other case I have experimented with in the past. The only problem I found with this case is high pressure and case life, which limited the velocity to around 2100 fps using a 215 gr bullet. Using a faster twist barrel like a 1-11 would limit the velocity to around 2000 fps before case life and accuracy suffered. I also would like to point out that using a faster twist than 1-15  in any case size in 30 caliber, limits the velocity and accuracy to about 30 fps slower for every 1 inch faster twist rate  For the last few years Mel Harris has done very well with this case using the MX4 bullet I designed for Don Eagan.

     I then used a 30 BR case with the shoulder set back so the case volume was the same as the PPC. The results were as good as the 6 PPC case with no problems with case life.

     Two years ago I was looking for something new to experiment with so I designed and built a mould for a 31 cal 215 gr bullet. The dimensions were 308 on the nose and 316 at the base. I used a 1-15  twist barrel  and opened  up a 30 BR case to accept the 31 caliber bullet. I shot the 31 caliber bullet at the 2005 nationals. It won the 100 yd 5 shot group agg. I only shot about 1000 bullets with this caliber and hope to test it more next summer.

     My future experiment next summer is to use the new 6.8 mm Remington case opened up to 30 and 31 caliber. The head diameter is about .020 smaller than the 6 PPC but is 1.680 long compared to the 30 PPC case which is only 1.500 long. This may have better case life than the 6 PPC case due to the larger case volume. If this new book is not published by the end of next summer I will send you my results."

John Ardito

     In my shooting and limited rifle building I have acquired some understanding of stability at long range but it isn't based on any research project as such.

     I have done some paper shooting at long range specifically to check for bullet yaw on out to 1000 yards and discussed the results with Doc Gunn who does real ballistic calculations and knows a great deal more than I ever will about the subject.

     This shooting and subsequent insights have resulted in my belief that Greenhill's constant should be adjusted to reflect velocity in order to assure stability at long range. That is, the 150 constant should be used if your velocity is 1500 ft/sec. In the shooting I do the velocity is commonly around 1300 - 1320 ft/sec so I use a constant of 132.

     Since I shoot pretty much exclusively at long range and have found good, consistent results by using this "adjusted" Greenhill I feel that it is a reliable way to calculate for twist when building or buying a rifle that will be used for shooting a bullet of a given weight and length over long range.

     Another way of saying it is that you should consult the formula, as adjusted, for velocity when considering something like a custom mold that pushes the length limit of the rifle you intend to shoot it in.

     For example I recently ordered a new Jones mold in 44. At 500 grains it is pretty long and even in my 1:16 twist 44/63 Ballard I had to up my load to assure stability at my distance of 1000 yards. It worked out just fine.

Forrest Asmus 

HOW TO MEASURE THE RATE OF TWIST OF A BARREL

     The maximum length bullet that a barrel will stabilize is determined primarily by the rate of twist of the barrel. Knowing the rate of twist of the barrel allows us to calculate how long a bullet can be stabilized by that barrel. (See “How to use the Greenhill formula”)

     The twist of a rifled barrel is measured in inches. A barrel with a 10" twist has grooves that make one revolution in 10 inches; a bullet fired through that barrel rotates once every 10 inches of forward travel.

     You'll need a pencil, a cleaning rod, a brush smaller than the bore, some cleaning patches, a roll of masking tape, and a yardstick or tape measure.

     Get the rifle stable, put it in a vice or on sand bags or somehow get it stable.

     A tightly patched cleaning rod will be rotated by the rifling as it is pushed through the barrel. If you measure how many inches the cleaning rod moves forward as it turns one revolution, you know the rate of twist of the rifling.

     Put the brush on the cleaning rod; .22 caliber brushes work from .30 to .38 caliber and .30 caliber brushes work for .40 to .45 caliber. Put one or more patches on the brush so the patched brush is a tight fit in the rifle bore. You want the cleaning rod to rotate with the rifling, and you don't want any slipping.

     Push the rod into the barrel from the muzzle. Put a small piece of the masking tape on the rod at the muzzle and mark it with the pencil. The mark should be a dot or a vertical line so that when the rod rotates one full turn the dot or line will be in the original position. Pull the cleaning rod out of the barrel until it has made one complete revolution, put another piece of masking tape on the cleaning rod and mark it at the muzzle. Measure the distance between pencil marks, and that is the number of inches the bullet must travel to make one revolution-the twist. (With a right hand twist, pulling the rod out of the barrel tends to tighten the brush on the rod. Pushing the rod in and measuring gives incorrect readings if the brush loosens on the rod.)

     Repeat this several times until you're comfortable that the result is accurate, and then Write It Down.

     John Bischoff: I use a plain spring type clothespin on the cleaning rod. When the clothespin has rotated all the way around – noon to noon or whatever – I’ve got a turn, and it’s easy to measure the inches if I started off with the clothespin touching the muzzle.

     Bill McGraw: I have used Cerrosafe to measure the twist of a barrel. I pour a long cast of 6-7” into the muzzle estimating more than half of the probable twist length. After removing the casting, and marking one groove at one end, measure the length when the same groove ends at exactly 180 degrees and double that length for the twist rate. Don’t be surprised if you get an odd number or even a fraction of standard twists.

THE GREENHILL FORMULA

     Twist is measured in the number of inches for one complete turn of the rifling in the barrel. For example, many 30 caliber rifles have barrels with a twist of one turn in 10 inches.

     For a given twist rate and diameter, there is a maximum length of bullet that may be stabilized.

     If the bullet is too long, or the twist is too slow, the bullet will not stabilize and will go through the target making a hole that is somewhere between oval and the side view of the bullet.

     When the bullet makes an oval hole, we say that it is “tipping”. When the hole starts to be real long and to look like a side view of the bullet, we say that the bullet is “keyholing”. It is not uncommon to find that best accuracy at slow velocities is accompanied by slight tipping of the bullet. (Tipping is also called "yawing")

     The Greenhill formula was designed around the stability = the ability to keep the sharp end going frontward, of low velocity lead bullets.

     Bullet stability is affected by several variables not included in the Greenhill formula.

     Bullet stability is slightly affected by velocity, faster bullets are slightly more stable than slower.

     Stability is affected by bullet density; an aluminum bullet won't be stable at Greenhill length and linotype (less dense) bullets are less stable than lead bullets.

     Stability is affected by the density of the medium the bullet is going through-generally air, but sometimes meat or water. Bullets are slightly more stable at high altitudes where the air is thin, than at sea level; and are much less stable going through denser mediums such as meat or water. Most of the time Greenhill does a remarkably good job of explaining the relationship between caliber, twist and bullet length required for bullet stability.

     The Greenhill formula is an approximation showing the relationship between rifling twist rate, maximum bullet length, and caliber. For any caliber and twist there is a maximum bullet length that will stabilize. For any caliber and bullet length there is a minimum rifling twist that will stabilize that bullet. By algebraic fiddling we can solve for either twist or length. Here is the formula set up to solve for maximum bullet length.

     The Greenhill Formula is:  L = (150/twist) * (caliber squared)

     Where L is the maximum length of bullet that will be stabilized in inches; twist is the number of inches required for one turn in the rifling; and caliber is the bullet diameter in inches.

     This table shows the maximum bullet length by caliber/twist combinations. For example, a .308 caliber barrel of 10" twist will stabilize a bullet that is a maximum of 1.42" long.

     Lead bullets weigh (very) approximately 82% as much as a lead cylinder with diameter = bullet caliber, and length = bullet length. Using this approximation, the table below shows the maximum weight of bullets which will be stabilized by a given twist/caliber combination. For example, a .308 caliber barrel of 10" twist will stabilize a bullet that weighs a maximum of 250 grains.

TWIST AND BLACK POWDER CARTRIDGE RIFLES

Dan Theodore

     Optimal Black Powder Cartridge Rifle (BPCR) cast bullet stability is a complex issue when shooting at extreme ranges. Not only bullet length but also grease groove design, nose length and nose-tip diameter have considerable affects on bullet stability for a given caliber and rifling twist-rate. Bullets are destabilized by the aerodynamic drag forces that act to induce yaw or even, at the extreme, produce tumbling bullets. The vector sum of all the drag forces acting on a bullet in flight is said to act at the center-of-pressure (CoP), which is some distance in front of the bullet's center-of-mass (CoM). The distance from the CoM to the CoP acts as a lever-arm to apply the force of the CoP about the CoM, which is what induces bullet yaw or wobble. The CoP acts to overturn the bullet by applying force perpendicular to the longitudinal axis of the bullet. This tends to make the bullet wobble or yaw. Above the transonic region drag goes by the velocity raised to the 1.7^th power. Within the transonic region drag is as high as the 6th power of the velocity. We can see that the overturning affects of the CoP go up quite rapidly for bullets that spend time in the transonic velocity region. That is why long, heavy for caliber cast bullet slugs require much faster twists than most would expect when they are shot over extreme ranges.

     Many thousands of rounds shot at 1,000-yds have shown that current thinking about cast bullet stability in the transonic region, 1.2 MACH down to 0.8 MACH (1,350 fps down to 900 fps) is somewhat lacking. The typical 45-caliber LR BPCR bullet shot in Creedmoor matches spends most of its time-of-flight in the transonic velocity range.

     Some of this lack of understanding precipitated from the use of Greenhill Formula derived twist-rates. Modifications to the Greenhill Formula have been undertaken by several cast bullet enthusiasts. The one developed by Charlie Dell is far superior to the original Greenhill Formula. But, even Charlie's enhancements do not capture the effects of grease groove design, nose length or nose-tip diameter on bullet stability. And, testing has shown that the predictive value of Charlie's reformulation of the Greenhill Formula degrades as the caliber decreases when long, heavy-for-caliber bullets are used. Its predictive value is high for 45-caliber bullets but does not have much predictive value for 38-caliber projectiles.

     Charlie's formula includes muzzle velocity, an improvement over the original formula. But, it does not capture the increased overturning moment that results from the increased MV that is particularly acute in the transonic range due to the much higher drag forces. It therefore overestimates the stabilizing affects of increased MV. Yaw angle testing from 10 yards to 1,000 yards has shown that increased MV is a poor substitute for appropriate twist-rate in the transonic velocity region.

The original Greenhill Formula is:

(150 x Caliber²) / Bullet Length = Required Twist Rate

Charlie Dell's Formula is:

(3.5 x MV^1/2 x Caliber²) / Bullet Length = Required Twist Rate

(NOTE: SEE THE APPENDIX FOR THE "C. DELL TWIST FORMULA WORKBOOK")

     Here is a simple example to show the predictive quality of both formulas. A 45-caliber, 1.460" long, 542-grain Paul Jones MiniGroove bullet, a highly stable bullet due to its long nose and very small grease grooves, is reasonably stable when an 18-twist barrel is used and the bullet launched at 1,250 fps. Most of the holes are round through the target when the rifle is fired from the 1,000-yd line. A faster twist would work better at the longer ranges when switching winds have to be contended with. The Greenhill formula predicts the required twist-rate as follows:

(150 x 0.458² )/ 1.460 = 21.55 inches per turn

     That twist is much to slow to produce a stable bullet at long range.

     Charlie Dell's modified equation predicts the following required twist-rate:

(3.5 x 1,250^1/2 x 0.458² )/ 1.460 = 17.8 inches per turn

     As we can see from the above calculations the Greenhill formula does not produce a useful result and the Dell equation is precise enough to be of value in determining the required twist-rate for the Paul Jones MiniGroove bullet. Using Dr. McCoy's stability software, a 17-twist produces a Stability Factor of 3.077 at 1,240 fps. After much testing a Stability Factor of 3.0 has been shown to be about optimum for long range BPCR projectiles. From experience to date, both the Dell and McCoy predictions are useful, but the use of a 17-twist barrel would give a slight advantage from the 1,000-yd line due to enhanced stability. Testing has shown that an 18-twist barrel is somewhat marginal for stabilizing the 1.460" long bullet when it is launched at 1,250 fps.

     Unlike high power bullets that stay above the transonic region all the way from the 1,000-yd line to the target, BPCR cast bullets loose stability with range. It has been shown though yaw angle testing that BPCR cast bullets can punch round holes though targets at 100 yards and then produce dramatically elliptical holes through 1,000-yd targets. For long range BPCR match shooting, bullets must be spun much faster than what is required for 200-yd paper punching or hunting. But, more is not always better when designing for optimum twist-rate. Too fast of a twist will degrade accuracy, while too slow of a twist will produce substantial bullet yaw that has been shown to cause wild flyers when less than stable air is the order of the day. Switching winds will wreak havoc on marginally stable bullets shot at long ranges. What optimum twist for a given caliber and bullet is, is still the subject of research and development. But, a simple working definition has been formulated. That simple working definition is:

Optimum bullet stability for BPCR cast bullets can be attained by using the slowest twist that will allow a given bullet to consistently produce round holes through the longest range target the bullet will be shot at.

     This definition assumes we are shooting though a target backed by corrugated cardboard.

     Currently, the best method this writer/rifle-crank has developed for determining optimum twist for a given bullet is to use Dr. Robert McCoy's stability program with modifications. For BPCR Silhouette distances a Stability Factor of about 2.5 is the design stability criterion. For matches that have targets past 800 yards a Stability Factor of 3.0 is used. One can also use the McCoy stability program to design an optimally stable bullet for a given caliber, barrel twist-rate, match distance(s) and design MV, the most oft way said software is used.